You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11?

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Quizplus · Accepted Answer

To achieve a portfolio with an expected return of 0.11, you can use the formula for the expected return of a portfolio: $E(R_p) = w_1E(R_1) + w_2E(R_2)$, where $E(R_p)$ is the expected return of the portfolio, $w_1$ and $w_2$ are the weights of the risky asset and the risk-free asset respectively, and $E(R_1)$ and $E(R_2)$ are their expected returns. Given $E(R_1) = 0.17$, $E(R_2) = 0.04$, and $E(R_p) = 0.11$, solving for $w_1$ gives $w_1 = 0.538$ or 53.8%, and consequently, $w_2 = 1 - w_1 = 46.2%$.

You Invest $1,000 in a Risky Asset with an Expected